Our third problem is designing market mechanisms for unilateral data sharing when agents have private types. The market is run by a social planner. We consider Vickrey-Clarke-Groves (VCG) mechanisms [1]}, which have been shown to uniquely implement social welfare at dominant strategies [2]}. However, VCG mechanisms are known to suffer from budget imbalance for the intermediary. We look for market mechanisms that have the following features: they implement approximate social-welfare-maximizing outcomes at dominant strategies, are individually rational, and are budget balanced. To this end, we propose a variation of the VCG mechanism which we refer to as mixed-VCG. Mixed-VCG uses both data distortion, referred to as data money, and monetary payment, to achieve budget balance while implementing social welfare via calibration to the value of budget imbalance of the standard VCG mechanism. Mixed-VCG uses downward distortion for budget surplus and upward distortion for budget deficit of the intermediary. While distorting data quality downward is practically at zero cost, for example by adding noise to the data, an upward distortion may be costly to the intermediary. To address this issue, we present a mechanism that we refer to as the distorted-mixed-VCG mechanism. Here the intermediary adds a fixed base downward distortion of data in a zero cost way, for example fixed noise added to data. Then instead of adding new data, the intermediary simply lifts controlled amounts of the fixed noise.
